$A$ and $B$ can separately complete a piece of work in $20$ days and $30$ days respectively. They worked together for some time,then $B$ left the work. If $A$ completed the rest of the work in $10$ days,then for how many days did $B$ work?

$A$ and $B$ can complete a piece of work in $12$ and $18 \text{ days}$ respectively. $A$ begins to do the work and they work alternatively one at a time for $1 \text{ day}$ each. The whole work will be completed in (in $\text{days}$):

$A$ can do a piece of work in $4 \, days$ and $B$ can do it in $12 \, days.$ In how many $days$ will they finish the work,both working together?

$A$ and $B$ complete a job in $12 \text{ days}$,while $A, B$,and $C$ can complete it in $8 \text{ days}$. $C$ alone will finish the job in (in $\text{days}$):

$A$ can do a piece of work in $16$ days and $B$ in $24$ days. They take the help of $C$ and all three together finish the work in $6$ days. If the total remuneration for the work is $Rs. 400$,what is the amount (in $Rs.$) each will receive in proportion to the work done?

If $16$ men or $20$ women can do a piece of work in $25$ days,in what time will $28$ men and $15$ women do it? (in days)